When I was in high school I operated the sound system for the auditorium (the second largest auditorium west of the Mississippi). This was/is a fantastic auditorium. The ceiling and down the walls was an acoustical mix, sort of like Cellotex. Any place that human hands could reach it was soon destroyed. "Hey, look at this. If you stick your finger in it, it leaves a hole." And, of course, everyone had to prove that for themselves.
The acoustical foam used in recording studios, radio stations, etc. is really great. However, if you stick your finger in it, you leave a hole. Need I say more. It is also VERY difficult to clean. Vacuums raise heck with it and it is totally impossible to dust or wash.
There have been quite a few research programs and studies seeking ways to break up the sound waves, sound reflections, etc. One simple one was window screen spaced a couple inches apart (like bread in a sandwich, air was the p-butter and jam). It was so effective that Chaffey College built a sound room in the middle of a very large classroom that way. They could broadcast within the "cage" while HS students were making their usual noises outside of the "cage." It is totally impractical for what you want however.
About 40 or 50 years ago a high school cafeteria was quieted by making frames out of 2 x 4s---like it was a frame around a window. Within the frame were some more 2 x 4s---like bars in the jailhouse window. As I remember these were about 4ft x 4ft. They were placed a few (2, 3, 4?) inches from the wall. They were placed a foot or two down from the ceiling; perhaps other places also---cannot remember. There was quite a bit of space between units. I have heard of that process being used other places but my memory won't tell me where. They were painted so they were not difficult to clean. I wonder if Google would have any thing on that? It was effective enough that there were some back page type news articles about how effective and economical it was for the school.
As Glenn says, "Remember dad, Google is your friend."
Glenn's rock band practiced in our, and other suckered parent's garages. They hung a couple layers of carped over the walls. It helped, however it was not professional quality sound control.
I don't know if that was any help. I just hope it gets your brain working so you hit Google, the public library, etc. I bet there is at least one acoustical design forum on the web.
Enjoy,
JimB